Lahenda ((23/9div3)^-2/94^2*frac{2/5})^-1

$$( \frac { ( 2 \frac { 3 } { 9 } \div 3 ) ^ { - 2 } } { \frac { 9 } { 4 } ^ { 2 } \cdot \frac { 2 } { 5 } } ) ^ { - 1 }$$

Arvuta

$$\frac{49}{40}=1,225$$

Lahenduse etapid

Avaldage \frac{\frac{2\times 9+3}{9}}{3} ühe murdarvuna.

$$\left(\frac{\left(\frac{2\times 9+3}{9\times 3}\right)^{-2}}{\left(\frac{9}{4}\right)^{2}\times \frac{2}{5}}\right)^{-1}$$

Korrutage 2 ja 9, et leida 18.

$$\left(\frac{\left(\frac{18+3}{9\times 3}\right)^{-2}}{\left(\frac{9}{4}\right)^{2}\times \frac{2}{5}}\right)^{-1}$$

Liitke 18 ja 3, et leida 21.

$$\left(\frac{\left(\frac{21}{9\times 3}\right)^{-2}}{\left(\frac{9}{4}\right)^{2}\times \frac{2}{5}}\right)^{-1}$$

Korrutage 9 ja 3, et leida 27.

$$\left(\frac{\left(\frac{21}{27}\right)^{-2}}{\left(\frac{9}{4}\right)^{2}\times \frac{2}{5}}\right)^{-1}$$

Taandage murd \frac{21}{27} vähimale ühiskordsele, eraldades ja taandades arvu 3.

$$\left(\frac{\left(\frac{7}{9}\right)^{-2}}{\left(\frac{9}{4}\right)^{2}\times \frac{2}{5}}\right)^{-1}$$

Arvutage -2 aste \frac{7}{9} ja leidke \frac{81}{49}.

$$\left(\frac{\frac{81}{49}}{\left(\frac{9}{4}\right)^{2}\times \frac{2}{5}}\right)^{-1}$$

Arvutage 2 aste \frac{9}{4} ja leidke \frac{81}{16}.

$$\left(\frac{\frac{81}{49}}{\frac{81}{16}\times \frac{2}{5}}\right)^{-1}$$

Korrutage \frac{81}{16} ja \frac{2}{5}, et leida \frac{81}{40}.

$$\left(\frac{\frac{81}{49}}{\frac{81}{40}}\right)^{-1}$$

Jagage \frac{81}{49} väärtusega \frac{81}{40}, korrutades \frac{81}{49} väärtuse \frac{81}{40} pöördväärtusega.

$$\left(\frac{81}{49}\times \frac{40}{81}\right)^{-1}$$

Korrutage \frac{81}{49} ja \frac{40}{81}, et leida \frac{40}{49}.

$$\left(\frac{40}{49}\right)^{-1}$$

Arvutage -1 aste \frac{40}{49} ja leidke \frac{49}{40}.

$$\frac{49}{40}$$

Lahuta teguriteks

$$\frac{7 ^ {2}}{2 ^ {3} \cdot 5} = 1\frac{9}{40} = 1,225$$